ELECTRONIC DESIGN NOTES - LOGIC GATES

Just
a few years ago,
logic gates
were regarded as the most advanced products in digital electronics. Today things went far, far ahead. The old
knowledge about logic gates, however, is still very important for hardware designers. If you want to become a true
specialist in hardware design, you need to start with the very roots, with the history of things.

The interesting aspect about logic gates is, they work exactly the same in hardware and in firmware. In other
words, you can build logic gates circuits in firmware, and they will work just as the hardware ones do, except for
being a bit slower in execution speed, naturally.

The structure employed to present (summarily) logic gates in this page is:

1. OR, AND, NOT GATES
A gate is a logic circuit performing one, simple Boolean function. Because they are used a lot, there are standard
families of gates-- this topic is going to be presented in Design Notes
#13.

Logic gates are presented here one at a time. To start, please be aware that
logic gates come as 2, 4, 6, or more
similar gates packed into one IC. Conventionally, pin 14 is wired high to VCC, and pin 7 is grounded.

The (electrical) input logic signals are marked in this page by A and B, and the output is (generally) marked as
C. The point to remember is, the output C is the result of a Boolean function.

AND, OR, NOT, LOGIC GATES

Picture

Truth Table

Description

A

B

C

0

0

0

0

1

0

1

0

0

1

1

1

Fig 1: AND Gate

The output C is:

C = A * B

A

B

C

0

0

0

0

1

1

1

0

1

1

1

1

Fig 2: OR Gate

The output C is:

C = A + B

A

A

1

0

0

1

Fig 3: NOT Gate

The output A is:

A = A

2. NAND, NOR GATES
NAND and NOR gates are the most used gates in logic circuits. It may be interesting to note that both of them
implement the NOT function, in addition to AND/OR: that is due to the fact
they were built out of NPN transistors (the silicon type). Fact is, the
NAND and NOR gates were the first ICs used to implement Combinational
Logic Networks.

NAND, NOR LOGIC GATES

Picture

Truth Table

Description

A

B

C

0

0

1

0

1

1

1

0

1

1

1

0

Fig 4:
NAND Gate

The output C is:

C = A * B

The NAND gate is equivalent to an OR gate having negated inputs

A

B

C

0

0

1

0

1

0

1

0

0

1

1

0

Fig 5:
NOR Gate

The output C is:

C = A + B

The NOR gate is equivalent to an AND gate having negated inputs

3. XOR GATES
The XOR gate is presented separately because we have discovered a few books
in which this
gate is explained incorrectly.
The XOR gate it is one of the most important, therefore it is mandatory to understand it very well.

XOR LOGIC GATE

Picture

Truth Table

Description

A

B

C

0

0

0

0

1

1

1

0

1

1

1

0

Fig 6: XOR Gate

The output C is:

C = A*B + B*A

4. MORE GATES FEATURES

1.
Some gates have an inhibit control pin--particularly the NOT ones. That is a very nice and useful feature.
2.
Some gates have a strobed input. If the strobe input is HIGH, the gate will function normally; if the
strobe is LOW, the output of the gate will remain in its last state.3.
There are basic gates built with expanders. An expander is an input pin implementing additional logic, thus
making the gate even more versatile.4.
Gates are commonly used to implement hardware time delay circuits. In addition, gates are used
to
set/reset hardware logic levels, and as clean pulse drivers.
5.
To end this, there are basic logic gates networks, built inside ICs, as are the AND-OR-Invert Registers,
plus many others. All logic gates are very useful basic modules, therefore this topic is developed
again in Electronic
Design Notes #13.